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arXiv:2507.22988

Probing Bound State Relaxation Dynamics in Systems Out-of-Equilibrium on Quantum Computers

Heba A. Labib, Goksu Can Toga, James K. Freericks, Alexander F. Kemper

Published Jul 30, 2025• 0 citations
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Abstract

Pump-probe spectroscopy is a powerful tool for probing response dynamics of quantum many-body systems in and out-of-equilibrium. Quantum computers have proved useful in simulating such experiments by exciting the system, evolving, and then measuring observables to first order, all in one setting. Here, we use this approach to investigate the mixed-field Ising model, where the longitudinal field plays the role of a confining potential that prohibits the spread of the excitations, spinons, or domain walls into space. We study the discrete bound states that arise from such a setting and their evolution under different quench dynamics by initially pumping the chain out of equilibrium and then probing various non-equal time correlation functions. Finally, we study false vacuum decay, where initially one expects unhindered propagation of the ground state, or true vacuum, bubbles into the lattice, but instead sees the emergence of Bloch oscillations that are directly the reason for the long-lived oscillations in this finite-size model. Our work sets the stage for simulating systems out-of-equilibrium on classical and quantum computers using pump-probe experiments without needing ancillary qubits.

DOI
10.48550/arxiv.2507.22988

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Pump-probe spectroscopy is a powerful tool for probing response dynamics of quantum many-body systems in and out-of-equilibrium. Quantum computers have proved useful in simulating such experiments by exciting the system, evolving, and then measuring observables to first order, all in one setting. Here, we use this approach to investigate the mixed-field Ising model, where the longitudinal field plays the role of a confining potential that prohibits the spread of the excitations, spinons, or domain walls into space. We study the discrete bound states that arise from such a setting and their evolution under different quench dynamics by initially pumping the chain out of equilibrium and then probing various non-equal time correlation functions. Finally, we study false vacuum decay, where initially one expects unhindered propagation of the ground state, or true vacuum, bubbles into the lattice, but instead sees the emergence of Bloch oscillations that are directly the reason for the long-lived oscillations in this finite-size model. Our work sets the stage for simulating systems out-of-equilibrium on classical and quantum computers using pump-probe experiments without needing ancillary qubits.
Pump–probe spectroscopy is a powerful tool for probing the response dynamics of quantum many-body systems in and out-of-equilibrium. Quantum computers have proved useful in simulating such experiments by exciting the system, evolving, and then measuring observables to first order, all in one setting. Here, we use this approach to investigate the mixed-field Ising model, where the longitudinal field plays the role of a confining potential that prohibits the spread of the excitations, spinons, or domain walls into space. We study the discrete bound states that arise from such a setting and their evolution under different quench dynamics by initially pumping the chain out of equilibrium and then probing various non-equal time correlation functions. Finally, we study false vacuum decay, where initially one expects unhindered propagation of the ground state, or true vacuum, bubbles into the lattice, but instead sees the emergence of Bloch oscillations that are directly the reason for the long-lived oscillations in this finite-size model. Our work sets the stage for simulating systems out-of-equilibrium on classical and quantum computers using pump–probe experiments without needing ancillary qubits.
The confinement of elementary particles and the decay of the false vacuum are two paradigmatic predictions of quantum field theory. In their simplest formulation, the two phenomena can be understood as two facets of an underlying symmetry-breaking mechanism: the degeneracy of a double-degenerate vacuum is lifted by adding an explicit symmetry-breaking external field. Confined states are false vacuum bubbles within a true vacuum (the true ground state of the model); likewise, false vacuum decay refers to the dissolution of the metastable vacuum through true vacuum bubbles nucleation via quantum tunneling. The interest in this area of research has been recently revamped by the advances in experimental techniques (e.g. trapped ions, ultracold atoms, Rydberg atoms): confinement has already proved to be accessible in condensed matter laboratory experiments while the direct laboratory study of the false vacuum decay is promisingly within reach. Moreover, in the past few decades the out-of-equilibrium dynamics of quantum many-body systems was promoted to the forefront of research in condensed matter physics. I will present relevant investigations of such phenomena in the context of quantum spin chain models through the observation of their real-time dynamics following a quantum quench (the paradigmatic theoretical and experimental protocol for non-equilibrium dynamics).
The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems.So far, however, experimental studies have focused on the relaxation dynamics of observables as described by the diagonal part of ETH, whose verification requires substantial numerical input.This leaves many of the general assumptions of ETH untested.Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations, which directly probe the off-diagonal part of ETH.We discuss and propose protocols to independently measure fluctuations and dissipations as well as higher order time-ordered correlation functions.We first show how the emergence of fluctuation-dissipation relations from a nonequilibrium initial state can be observed for the two-dimensional (2D) Bose-Hubbard model in superconducting qubits or quantum gas microscopes.Then we focus on the long-range transverse field Ising model (LTFI), which can be realized with trapped ions.The LTFI exhibits rich thermalization phenomena: For strong transverse fields, we observe prethermalization to an effective magnetization-conserving Hamiltonian in the fluctuation-dissipation relations.For weak transverse fields, confined excitations lead to nonthermal features, resulting in a violation of the fluctuation-dissipation relations up to long times.Moreover, in an integrable region of the LTFI, thermalization to a generalized Gibbs ensemble occurs and the fluctuation-dissipation relations enable an experimental diagonalization of the Hamiltonian.Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
We consider non-equilibrium dynamics after quantum quenches in the mixed-field three-state Potts quantum chain in the ferromagnetic regime. Compared to the analogous setting for the Ising spin chain, the Potts model has a much richer phenomenology, which originates partly from baryonic excitations in the spectrum and partly from the various possible relative alignments of the initial magnetisation and the longitudinal field. We obtain the excitation spectrum by combining semi-classical approximation and exact diagonalisation, and we use the results to explain the various dynamical behaviours we observe. Besides recovering dynamical confinement, as well as Wannier-Stark localisation due to Bloch oscillations similar to the Ising chain, a novel feature is the presence of baryonic excitations in the quench spectroscopy. In addition, when the initial magnetisation and the longitudinal field are misaligned, both confinement and Bloch oscillations only result in partial localisation, with some correlations retaining an unsuppressed light-cone behaviour together with a corresponding growth of entanglement entropy.
We consider non-equilibrium dynamics after quantum quenches in the mixed-field three-state Potts quantum chain in the ferromagnetic regime. Compared to the analogous setting for the Ising spin chain, the Potts model has a much richer phenomenology, which originates partly from baryonic excitations in the spectrum and partly from the various possible relative alignments of the initial magnetisation and the longitudinal field. We obtain the excitation spectrum by combining semiclassical approximation and exact diagonalisation, and we use the results to explain the various dynamical behaviours we observe. Besides recovering dynamical confinement, as well as Wannier-Stark localisation due to Bloch oscillations similar to the Ising chain, a novel feature is the presence of baryonic excitations in the quench spectroscopy. In addition, when the initial magnetisation and the longitudinal field are misaligned, both confinement and Bloch oscillations only result in partial localisation, with some correlations retaining an unsuppressed light-cone behaviour together with a corresponding growth of entanglement entropy.
The false vacuum decay has been a central theme in physics for half a century with applications to cosmology and to the theory of fundamental interactions. This fascinating phenomenon is even more intriguing when combined with the confinement of elementary particles. Due to the astronomical timescales involved, the research has so far focused on theoretical aspects of this decay. The purpose of this Letter is to show that the false vacuum decay is accessible to current optical experiments as quantum analog simulators of spin chains with confinement of the elementary excitations, which mimic the high energy phenomenology but in one spatial dimension. We study the nonequilibrium dynamics of the false vacuum in a quantum Ising chain and in an XXZ ladder. The false vacuum is the metastable state that arises in the ferromagnetic phase of the model when the symmetry is explicitly broken by a longitudinal field. This state decays through the formation of ``bubbles'' of true vacuum. Using infinite volume time evolving block decimation (iTEBD) simulations, we are able to study the real-time evolution in the thermodynamic limit and measure the decay rate of local observables. We find that the numerical results agree with the theoretical prediction that the decay rate is exponentially small in the inverse of the longitudinal field.